Science:Math Exam Resources/Courses/MATH110/December 2017/Question 03 (b)
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Question 03 (b) 

Evaluate the following limits or determine they are either infinite or do not exist. (b) 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

What are the limits of the numerator and the denominator, respectively? 
Hint 2 

Factorize and look for cancellations. 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let and . Since they are (quadratic) polynomials and are therefore continuous everywhere, we compute and This means that both and carry a common factor of . In order to cancel such factor, we write and Then for any real number , we have In particular, the given limit is Answer: . 